At what height from the surface of earth will the value of g be reduced by `36%` from the value on the surface? Take radius of earth `R = 6400 km`.

Explanation

Let `h` be the height at which the value of `g` be reduced by `36%`, i.e., the value of `g` at height `h` is `g' = 100 - 36 = 64%` of the earth's value
Hence `g' = (64)/(100)g`
Now `g' = (gR^(2))/((R + h)^(2)) = (64)/(100) g` or `(R )/(R + h) = (8)/(10)`
or `h = (R )/(4) = (6400)/(4) = 1600 km`